​En lineas generales, el texto es comprensible, sólo que hay ciertas partes donde no logro captar las ideas. Bueno como es lógico las correcciones están puestas en paréntesis, la mayoría de ellas son sustituciones y algunas otras son eliminaciones de ciertas palabras. Disculpa si no logré entender bien lo que quisiste colocar e hice correcciones por mero desconocimiento, pero creo que la mayoría son justas.
Espero tus correcciones... Suerte!

Luis Escalona =)




Classification



Classical Probability: The classical probability is that it takes an objective and may be viewed in two ways: a priori and a posteriori.
(You can rewrite this part because it's kinda difficult to understand. You can delete this phrase, and continue with "takes".... The classical probability, takes an..................or put this. This type of probability takes an objective etc etc etc...)


° Prior probabilities: The probability of an event A, P (A), is the measure of the chance that (When) this event will (delete) occurs.
In this case the results of the experiment are equal
likely (delete). This method was developed by Laplace.



P(A)= # of ways A can occur / # total possible outcomes.



P(A) = A (events corresponding to A) / S (total events in the sample space).




° Posterior probability:
In the case that events do not have equal chance of occurrence, the problem of assigning probabilities happens to posterior.
If an experiment is performed a large number of (repeated) times, N times for example, let n be the number of times that happens an event E. Then experimentally observed that as (Change this part) N increases the n / N tends to a stable value p. This value p is called the probability of E and we write p (E).



Subjective Probability: It refers to the probability of occurrence of an event based on previous experience(s), personal opinion, knowledge or intuition of the(an) individual. In this case, after studying the information available, (it) is assigned a value of probability to events based on our degree of belief that the event might occur.



Frequentist probability:Repeating an experiment under the same conditions many times and repeat until it reach almost classical probability (Guess this part could be written in other form. I can't catch this one, sorry :$:$:$). It applies to randomized experiments that can be repeated under the same conditions the number of times desired.



Comparison & Contrast


Both, the classical and the frequentist definition are based on random repetition of the(an) experiment, but there are many experiments that can not be repeated under the same conditions and, therefore, can not apply the objective interpretation of probability. In such cases, it is necessary to see an alternative view, which isn’t depend(s) of(on) repetition, so when applying subjective probability that is different of the other two, (it's possible to) make a personal opinion in which different observers may have different(various) degrees of belief about possible outcomes, equally valid.